Digital Signal Processing Reference
In-Depth Information
Im
3
2
s
1
1
s
3
s
1
s
2
3
2
1
0
1
2
3
4
5
Re
s
2
1
2
(a)
Im
3
2
s
4
s
1
s
2
1
s
1
s
2
3
2
1
0
1
2
3
4
5
Re
s
2
1
2
(b)
Figure D.2
Complex number addition and
subtraction.
The difference of the two complex numbers is illustrated by
s
4
= s
1
- s
2
= (2 + j2) - (3 - j1) =-1 + j3.
In subtraction, the real part of the difference is equal to the difference of the real
parts, and the imaginary part of the difference is equal to the difference of the imag-
inary parts. This subtraction in the complex plane is illustrated in Figure D.2(b) and
can be considered to be the addition of and Note that the negative of a com-
plex number in the complex plane is that complex number rotated by
The rules of real multiplication apply to complex multiplication, with the
values of powers of
j
given by (D.3). For example, let
s
1
-s
2
.
180°.
s
5
be the product of
s
1
and s
2
